The French Open champion needed just 58 minutes to send world number 252 Burdette packing.
"I expected her to play a big, solid match," said Sharapova, the 2006 US Open champion. "She came out, she has pretty huge groundstrokes, and she likes to go for it.
"She's certainly somebody who could be dangerous if you give her the time to do what she likes to do."
Burdette, a 21-year-old wild card entry into the tournament, did not have time to do much of anything as she was swept off the court in 58 minutes.
Sharapova, who has lost just seven games in her first three matches, now plays Russian compatriot Nadia Petrova, a 6-4 7-5 winner over Czech Lucie Safarova.
Despite missing the hardcourt run-up to Flushing Meadows, Sharapova is playing as well as anyone in the women's draw.
"I didn't know too much going into this event because I hadn't played on hard in a few months," she said. "That made me extra focused, and I wanted to really get going from the beginning and be aggressive.
"Took a little bit of a break after Wimbledon and went home. I kind of recharged a little bit. Certainly feel a lot more energy than I did maybe after the French (Open)."
Sharapova said Petrova has "been playing really good tennis."
"She's someone that likes the faster courts, especially in New York," said Sharapova, who owns a 8-1 lifetime mark against Petrova. "I have had some tough matches against her.
"Although I have a good record, they have always been really tough and have gone to some three-setters, some tough two-setters.
"She has a big game, great serve, a difficult opponent, but I'm looking forward to that challenge."
Top seed Victoria Azarenka swept past China's Zheng Jie 6-1 6-0 in less than an hour to advance to the fourth round.
The Australian Open champion took just 59 minutes to set up a contest with Georgia's Anna Tatishvili, who beat Luxembourg's Mandy Minella 7-5 6-0, for a place in the quarter-finals.
Belarusian Azarenka has lost only six games in her first three matches at Flushing Meadows.
Champion Sam Stosur, seeded seven at Flushing Meadows, came through the first real test of her title defence as she beat American Varvara Lepchenko 7-6 6-2.
The first set was a dogfight but the seventh seed took the tie-break and then lifted her game to romp through the second set.
Stosur was broken in the opening game of the match, setting the tone for a gruelling first set, which lasted 59 minutes.
But the Australian snatched it 7-5 to move ahead and with the pressure off, she ran through the second to reach the last 16, where she will meet Britain's Laura Robson, a surprise 6-4 6-7(5) 6-2 winner over China's Li Na.
Number five seed Petra Kvitova will meet 11th seed Marion Bartoli in the final fourth round match-up to be decided on Friday.
Czech Kvitova downed Pauline Parmentier without too much fuss 6-4 6-4 while Bartoli of France saw off compatriot Kristina Mladenovic in similarly comfortable fashion 6-2 6-4.